Identification of a New Form of Electron Coupling in the ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ Superconductor by Laser-Based Angle-Resolved Photoemission Spectroscopy

Laser-based angle-resolved photoemission measurements with superhigh resolution have been carried out on an optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_8$ high temperature superconductor. New high energy features at $\sim 115\mathrm{meV}$ and $\sim 150\mathrm{meV}$, in addition to the prominent $\sim 70\mathrm{meV}$ one, are found to develop in the nodal electron self-energy in the superconducting state. These high energy features, which cannot be attributed to electron coupling with single phonon or magnetic resonance mode, point to the existence of a new form of electron coupling in high temperature superconductors.

Figure 1

Electron dynamics of optimally doped Bi2212 ($T_c=91\mathrm{K}$) measured along the $\Gamma (0,0)-Y(\pi ,\pi )$ nodal direction at 17 K. (a) Raw image showing photoelectron intensity (represented by false color) as a function of energy and momentum. The inset shows the location of the momentum cut in the Brillouin zone; (b) nodal dispersion extracted from (a) by fitting MDCs. The dotted line connecting the two energy positions in the dispersion at the Fermi energy and $-0.4\mathrm{eV}$ is an empirical bare band for extracting the effective real part of self-energy in Fig. 2b. The inset shows the corresponding MDC width (FWHM).

Figure 2

Momentum dependence of dispersions (a) and corresponding effective real part of electron self-energy (b). The inset of (a) shows the location of momentum cuts in the Brillouin zone. The effective self-energy in (b) is obtained by taking the straight line connecting two positions in dispersion at the Fermi energy and $-0.4\mathrm{eV}$ as a bare band. The arrows in (b) mark fine features at $\sim 70\mathrm{meV}$, 115 meV, and 150 meV, and a possible feature near 94 meV. For clarity, curves in (a) are offset along the momentum axis, while curves in (b) are offset along the vertical axis; the offset values are given in the legends.

Figure 3

Temperature dependence of the nodal MDC dispersion (a) and MDC width (b). The top-left inset of (a) plots the momentum value as a function of temperature at four typical energies: $E_F$ [empty (red) circle], $-0.07\mathrm{eV}$ [solid (green) circle], $-0.2\mathrm{eV}$ [empty (blue) square], and $-0.3\mathrm{eV}$ [solid (black) circle] obtained by averaging over the $\pm 10\mathrm{meV}$ energy range. The bottom-right inset of (a) shows MDCs at these four energies measured at 17 K (solid line) and 128 K (dashed line). (c) The difference of the MDC width between two temperatures at 17 K and 128 K. The arrows in (b) and (c) mark possible features showing up in the scattering rate.

Figure 4

(a) Temperature dependence of the effective real part of electron self-energy extracted from dispersions in Fig. 3a by taking a straight line as a bare band connecting two points at $E_F$ and $-0.4\mathrm{eV}$ on the dispersion at 128 K. (b) Temperature dependence of the difference between the measured self-energy in (a) and the fitted one for 128 K [solid black line in (a)]. The 128 K self-energy is fitted by polynomials and used to reduce statistical errors.